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%I #14 Feb 27 2021 11:21:19
%S 1,6,14,20,30,40,36,48,62,42,72,100,68,120,112,48,126,108,98,180,136,
%T 160,180,144,132,126,216,200,240,280,112,192,254,120,252,320,210,360,
%U 324,144,264,252,288,420,340,280,336,288,260,342,294,360,408,520,360,240,496
%N Number of integer solutions to a^2 + b^2 + c^2 + 2*d^2 = n.
%H Seiichi Manyama, <a href="/A236928/b236928.txt">Table of n, a(n) for n = 0..10000</a>
%H J. Zucker, <a href="https://doi:10.3390/sym9120314">Exact Evaluation of Some New Lattice Sums</a>, Symmetry, 2017, 9(12), 314.
%F G.f.: theta_3(q)^3*theta_3(q^2), where theta_3() is the Jacobi theta function. - _Ilya Gutkovskiy_, Aug 01 2018
%F G.f.: 1 + 8*Sum{n >= 1} n*(q^n - q^(3*n) - q^(5*n) + q^(7*n))/(1 - q^(8*n)) - 2*Sum_{n >= 0} (-1)^((n^2+n)/2)*(2*n+1)q^(2*n+1)/(1 - q^(2*n+1)). See Zucker p. 5. Cf. A117000. - _Peter Bala_, Feb 25 2021
%p See A236924.
%Y For number of solutions to a^2+b^2+c^2+k*d^2=n for k=1, 2, 3, 4, 5, 6, 7, 8, 12 see A000118, A236928, A236926, A236923, A236930, A236931, A236932, A236927, A236933.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, Feb 15 2014
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